1. LLRF FOR CRAB CAVITIES A FEW SELECTED ISSUES AND RELEVANT EXPERIENCE FROM THE LHC MAIN CAVITIES (ACS) P. Baudrenghien CERN BE-RF 2 nd HiLumi LHC/LARP Frascati, Nov 15,2012

2. COUPLED BUNCH (IN)STABILITY Reduction of Cavity Impedance at the fundamental mode HiLumi LHC/LARPFrascati, Nov. 15, 2012

3. RF feedback With accelerating cavities, in high beam current machines, the problem of (in)stability caused by the cavity impedance at the fundamental is now routinely cured by active feedback. The amplifier driven by a feedback system feeds a current into the cavity which attempts to cancel the beam current The cavity impedance is effectively reduced by the feedback gain The limitation comes from the unavoidable delay in the loop. Above some gain level the delay will drive the feedback into electrical oscillations (not related to the beam) HiLumi LHC/LARPFrascati, Nov. 15, 2012

4. With an RF feedback the minimal effective impedance R min and closed-loop single-sided bandwith  scale with loop delay T For the LHC, we have T=650 ns R min = 75 k  /cavity, 0.6 M  total  /2  = 320 kHz Strong RF feedback. The LHC ACS Measured Closed Loop response with the RF feedback. Q L =60000 without feedback (~7 kHz 2-sided BW). With feedback we get 700 kHz BW. The effective impedance is reduced by ~ 35. The LHC cavities are equipped with movable couplers and Q L can be varied from 10000 to 100000. But, with feedback, Q eff ~600 in all positions. The loop delay T was kept low in the LHC ACS HiLumi LHC/LARP With the RF feedback we reduce the ACS cavity impedance at resonance by ~35 linear (Q L =60k). The 21.6 M  are reduced to 0.6 M . Frascati, Nov. 15, 2012

5. RF feedback on the Crab Cavity Q L =10 6, 1  s loop delay, 150 ns TX group delay RF feedback gain = 350 linear. Impedance reduced by 50 dB The open loop phase must be changed with the detuning. Not a problem. We do similar adjustment for the ACS, when changing Main Coupler Position HiLumi LHC/LARP Cavity impedance with and without RF feedback. Left: situation in physics with CC on tune Right: situation during filling, ramping, squeeze, adjust, with CC detuned by -100 kHz Frascati, Nov. 15, 2012

6. ACTUALLY THE IMPEDANCE REDUCTION CAN BE LARGER THAN THE FEEDBACK GAIN HiLumi LHC/LARPFrascati, Nov. 15, 2012

7. NB resonator, longitudinal and transverse Longitudinal impedance of a longitudinal mode The growth rate and tune shift of coupled-bunch mode l (dipole only) can be computed from the cavity impedance With  =(p M+l)  rev +  s. HiLumi LHC/LARP Transverse impedance of a transverse mode The growth rate and tune shift of coupled-bunch mode l (dipole only) can be computed from the cavity impedance With  =(p M+l)  rev +  b. Frascati, Nov. 15, 2012

8. NB resonator, longitudinal HiLumi LHC/LARP With 25 ns bunch spacing (M=3564), and a resonance around 400 MHz, with BW below 40 MHz (with feedback), the infinite sum reduces to two terms (p= ±10) The growth rate is computed from the difference between real impedance on the two ±(l  rev +  s ) sidebands of the  RF Much reduced if the real part of the effective impedance is symmetric around  RF. That is the case if the detuning is small compared to the closed loop BW (LHC ACS). Frascati, Nov. 15, 2012

9. Again, with 25 ns bunch spacing (M=3564), a resonance around 400 MHz, with a BW below 40 MHz, the infinite sum reduces to the two terms (p= ±10) Again, the growth rate is computed from the difference between real impedance on the two ±(l  rev +  b ) sidebands of the  RF For example, with Q b =60.3, the growth rate of mode l=-60 is computed from the difference between the real part of the impedance at ±0.3  rev But is the real part of the effective impedance symmetric around  RF ? NB resonator, transverse HiLumi LHC/LARPFrascati, Nov. 15, 2012

10. RF feedback on the Crab Cavity Q L =10 6, 1  s loop delay, 150 ns TX group delay, 1 M  /m RF feedback gain = 350 linear HiLumi LHC/LARP Real part of the cavity impedance with RF feedback. Left: situation in physics with CC on tune Right: situation during filling, ramping, squeeze, adjust, with CC detuned by -100 kHz Important reduction to be expected in physics No reduction when cavity is parked (-100 kHz) Frascati, Nov. 15, 2012

11. SO WHAT IF THE IMPEDANCE IS STILL TOO HIGH? HiLumi LHC/LARPFrascati, Nov. 15, 2012

12. Longitudinal: One-Turn delay feedback (OTFB) on ACS The One-Turn delay Feedback (OTFB) produces gain only around the revolution frequency harmonics It further reduces the transient beam loading and effective cavity impedance (factor of 10) Effective Cavity Impedance with RF feedback alone (smooth trace) and with the addition of the OTFB (comb). The cavity centre frequency is 400.789 MHz. We look at a band offset by +200 kHz to +300 kHz. Frev= 11 KHz. The OTFB provides ~ 20 dB additional impedance reduction on the Frev lines. HiLumi LHC/LARP With the One-Turn delay feedback ACS we gain another factor 10 in impedance reduction on the revolution sidebands resulting in a 350-fold reduction (Q L =60k). The 21.6 M  are now reduced to 0.06 M  Frascati, Nov. 15, 2012

13. Transverse: Betatron Comb filter One-turn delay filter with gain on the betatron bands To keep 10 dB gain margin, the gain on the betatron lines is limited to ~ 6 linear (16 dB) 2 N Poles on the betatron frequencies Reduction of noise PSD where the beam responds Reduction of the effective cavity impedance thereby improving transverse stability Zeros on the revolution frequency lines No power wasted in transient beam loading compensation with off centered beam Betatron comb filter response with a=31/32 and non-integer Q=0.3. Observe the high gain and zero phase shift at (n ±0.3) frev HiLumi LHC/LARP Some details in CC11 presentation. Study ongoing… Commission in the SPS Frascati, Nov. 15, 2012

14. Coupled feedback For perfect closure of the orbit and to minimize the overall effect of one-cavity fault, we look at the possibility of coupled feedback Taking a pair of cavities on each side of a given IP (crabbing and un-crabbing), we wish to keep the two voltages equal That can be done if the FDBK for a given TX considers also the voltage difference V 2 -V 1 Two cavities on opposite sides of an IP: We wish to regulate the individual voltages AND the voltage difference. HiLumi LHC/LARP Some details in CC11 presentation. Study ongoing… Loop delays critical… Commission in the SPS Frascati, Nov. 15, 2012

15. BUT THAT HAS NO EFFECT ON THE HOM/LOM HiLumi LHC/LARPFrascati, Nov. 15, 2012

16. RF NOISE Random noise only. Assuming perfect beam loading compensation. HiLumi LHC/LARPFrascati, Nov. 15, 2012

17. Architecture We propose to drive the Crab Cavities from the RF reference (Beam Control, VCXO out), and count on strong RF feedback to set the demanded field in the cavities Crab cavities B2 driven from RF reference B2 Crab cavities B1 driven from RF reference B1 HiLumi LHC/LARPFrascati, Nov. 15, 2012

18. Beam Control plus Cavity Controller LHC ACS Two major noise sources: The RF reference noise from the Beam Control, introduced during the modulation/demodulation process in the Cavity Controller. This noise is coherently injected in all cavities The noise injected in the Cavity Controller electronics and the Klystron noise. This noise is uncorrelated from cavity to cavity HiLumi LHC/LARPFrascati, Nov. 15, 2012

19. Cavity RF Noise  RF feedback noise sources:  The RF reference noise n ref  The demodulator noise (measurement noise) n meas  The TX (driver) noise n dr. It includes also the LLRF noise not related to the demodulator  The Beam Loading I b  x  We get Closed Loop response CL(s)  Equal to ~1 in the CL BW  Increase of K increases the BW  Within the BW, reference noise and measurement noise are reproduced in the cavity field Beam Loading response = effective cavity impedance Zeff(s)  Equal to ~1/KG in the CL BW  Increase of K decreases Zeff within the CL BW  Within the CL BW, TX noise and beam loading are reduced by the Open Loop gain KG Main coupler HiLumi LHC/LARPFrascati, Nov. 15, 2012

20. RF noise without beam. ACS 50 Hz and harmonics come from the klystron HV ripples. The klystron loop reduces them by 50 dB up to 600Hz. Fs crosses 50 Hz during the ramp [55 Hz – 26 Hz]. n dr noise In the 10kHz-400 kHz range the noise level is defined by the demodulation of the antenna signal in the RFfdbk and OTFB loops. Flat between -135 and - 140 dBc/Hz. n meas noise SSB phase noise Power Spectral Density in dBc/Hz. RF sum of the 8 cavities beam 1. No beam but physics conditions (12 MV). The grey trace corresponds to injection conditions (6 MV). Out of loop measurement. The dips at multiple of Frev are the action of the OTFB that increases regulation gain and decreases noise level HiLumi LHC/LARP In the transverse plane the first betatron band is at 3 kHz. Reference noise is not an issue. The performances will be defined by TX noise and measurement noise Noise in the 10Hz-1kHz range is caused by the VCXO limited Q (-20 dB/decade). n ref noise Frascati, Nov. 15, 2012

21. The beam will sample the noise in all betatron side-bands The integrated effect of the measurement noise increases with the closed loop BW, that is proportional to the feedback gain HiLumi LHC/LARP Scaling the ACS to crab Assume a SSB phase noise of L= -135 dBc/Hz or S= 6.3E-14 rad 2 /Hz Now summing the noise PSD from DC to + 300 kHz over all betatron bands, we get 300/11 x 2 x 6.3E-14 rad 2 /Hz =3.4E-12 rad 2 /Hz from DC to the revolution frequency Conclusion: a “copy” of the LHC ACS design (300 kW klystron !) would generate 3.7E-8 rad 2 white noise That is 2E-4 rad rms or 1.1E-2 deg rms phase noise @ 400 MHz SSB phase noise in an ACS cavity with varying feedback gains. Measured and calculated [1] Frascati, Nov. 15, 2012 But what counts is the power in the betatron band only

22. Trade-off for CCs A weak coupling (large Q L ) Reduces the effect of TX and LLRF noise. Good Make cavity field sensitive to mechanical vibrations. Bad A large feedback gain Reduces the instability growth rates. Good Limits the effect of TX and LLRF noise. Good Increases the integrated effect of measurement noise by increasing the BW. Bad Trade-off required Will depend on the TX noise HiLumi LHC/LARP First Hadron machine with CCs…. First Hadron machine with klystrons Frascati, Nov. 15, 2012 Importance of the SPS test-bench

23. EMITTANCE GROWTH MEASUREMENT HiLumi LHC/LARPFrascati, Nov. 15, 2012

24. How can we measure the effect of RF noise if it is not dominant in the emittance growth? We faced a similar problem in the LHC as longitudinal emittance growth driven by IBS is much stronger than the growth caused by RF noise Measurements were done with ions at 3.5 Z TeV in Nov 2010 with four equi-distant bunches per ring [1] HiLumi LHC/LARPFrascati, Nov. 15, 2012

25. Phase noise was injected in one RF cavity, with a bandwidth of 10 Hz, centered on the first revolution band: f rev ±f s The power of the injected noise was varied during the test Bunch length was monitored With large noise power, the effect became dominant, allowing for a good calibration of emittance growth (slope of bunch lengthening) vs RF noise power HiLumi LHC/LARP Will be done on the SPS test-bench f rev Frascati, Nov. 15, 2012

26. HARDWARE HiLumi LHC/LARPFrascati, Nov. 15, 2012

27. For each Crab Cavity we have a Cavity Controller including: An RF Feedback Loop for noise and beam loading control A TX Polar Loop to reduce the TX noise and stabilize its gain/phase shift A Tuner Loop to shift the cavity to a detuned position during filling and ramping. Then smoothly bring the cavity on-tune with beam for physics A field Set Point for precise control of the cavity field. Field control fully integrated with the rest of the LHC by using standard FGCs (slides 22-23) Interconnection with the paired cavity(ies) Coupled feedback Measurement of bunch phase modulation Gain increased on the betatron bands HiLumi LHC/LARPFrascati, Nov. 15, 2012

28. HiLumi LHC/LARP SSB Modulator IF (I & Q) ≈25MHz Dual TxDac 16 bits RF Demodulator RF&LO mixing IF ≈25MHz 14 bits ADC Fs=4 · IF ≈100MHz 4x LO Distribution 2 x Duplex Optical Serial Links 2 in & 2 out 2Gbits/s ( ≤ 3.2Gbits/s) SRAM 2x8 Mbyte for diagnostics VME P1 backplane for slow controls/read out Dedicated backplane (P2): Power Supply Clocks Interlocks … Xilinx Virtex 5 SX G. Hagmann BE-RF-FB designer SPS 800 MHz TWC prototype Frascati, Nov. 15, 2012

29. HiLumi LHC/LARP 2 x Duplex Optical Serial links 2 inputs 2 outputs Status LED RF output RF inputs (4x) LO input G. Hagmann BE- RF-FB designer SPS 800 MHz TWC prototype Frascati, Nov. 15, 2012

30. HiLumi LHC/LARP ACS LLRF. 1 rack/ 2 VME crates per cavity in a Faraday Cage in the UX45 cavern Frascati, Nov. 15, 2012

31. HiLumi LHC/LARP ACS RF in the UX45 cavern Faraday cages with LLRF electronics Klystrons Waveguides to cavities Concrete shielding around the beam line Frascati, Nov. 15, 2012

32. Operational scenario HiLumi LHC/LARPFrascati, Nov. 15, 2012

33. Operational scenario (revisited) Strong RF feedback and tune controls are ON at all time During filling, ramping or operation with transparent crab cavities, we detune the cavity but keep a small field requested for the active Tuning system. If the crab kick is provided by a pair of cavities we could use counter-phasing to make the small cavity field invisible to the beam. Else amplitude/phase can be optimized among the cavities of same Beam/IP to minimize effects. The RF feedback is used with the cavity detuned to provide stability and keep the Beam Induced Voltage zero if the beam is off-centered. We can use the demanded TX power as a measurement of beam loading to guide the beam centering ON flat top Reduce the detuning while keeping the voltage set point very small. The RF feedback keeps the cavity impedance small (beam stability) and compensates for the beam loading as the cavity moves to resonance Once the cavity detuning has been reduced to zero, use the functions to synchronously change the voltage in all crab cavities as desired. Any luminosity leveling scheme is possible. HiLumi LHC/LARPFrascati, Nov. 15, 2012

34. CONCLUSIONS HiLumi LHC/LARPFrascati, Nov. 15, 2012

35. We propose to use a strong RF feedback around the CC By reducing the effective cavity impedance by orders of magnitude, the requirements for the Transverse Damper are relaxed It strongly reduces the TX noise It provides for precise control of the crabbing voltage It calls for a compact layout It brings requirements on the TX: linearity, BW, group delay It has no effect on HOMs RF noise Optimization depends on the importance of TX noise compared to measurement (antenna demodulation) The tuning with very low field (much smaller than beam loading) must be solved. We will study the system used on the SC 352 MHz cavity installed in the SPS for e+e- [2][3] The SPS test is essential HiLumi LHC/LARPFrascati, Nov. 15, 2012

36. REFERENCES HiLumi LHC/LARPFrascati, Nov. 15, 2012

37. [1] T. Mastoridis et al., Radio Frequency noise effects on the CERN Large Hadron Collider beam diffusion, PRST AB, 14, 092802 (2011) [2] D. Boussard et al., RF Feedback applied to a Multicell Superconducting Cavity, EPAC 1988 [3] F. Pedersen, A novel RF cavity tuning feedback scheme for heavy beam loading, IEEE NS-32, No 5, Oct. 1985 Frascati, Nov. 15, 2012High Lumi LHC

38. BACK-UP SLIDES HiLumi LHC/LARPFrascati, Nov. 15, 2012

39. Higher beam intensity: stability With the strong RF feedback and OTBF, the cavity impedance at the fundamental can easily accept 2.2E11 p/bunch, 25 ns spacing Momen tum (GeV/c) QLDetuning (kHz) Total RF Voltage (MV) Synchr otron Freque ncy (Hz)  max without fdbk (s-1)  max with RFfbk and OTFB (s-1)  s /4 (s-1) 45020000-12.5 (half) 654.81500.0613.3 45020000-19.8 (full) 654.81500.0713.3 700060000-9.9 (full)1219.8800.014.8 Calculations done for after LS1 conditions: 2835 bunches, 2.2E11 p/bunch, 25 ns spacing, 1.25 ns, 1.12 A DC Growth rate of the coupled-bunch mode. Max over all modes Landau damping limit (1/4 tune spread) HiLumi LHC/LARPFrascati, Nov. 15, 2012

40. Architecture We propose to drive the Crab Cavities from the RF reference (Beam Control, VCXO out), and count on strong RF feedback to set the demanded field in the cavities Crab cavities B2 driven from RF reference B2 Crab cavities B1 driven from RF reference B1 HiLumi LHC/LARPFrascati, Nov. 15, 2012

41. RF phase modulation In physics We will accept the modulation of the cavity phase by the beam current (transient beam loading) and adapt the voltage set point for each bunch accordingly The klystron drive is kept constant over one turn (amplitude and phase) The cavity is detuned so that the klystron current is aligned with the average cavity voltage Needed klystron power becomes independent of the beam current. For Q L =60k, we need 105 kW only for 12 MV total Stability is not modified: we keep the strong RFfdbk and OTFB The resulting displacement of the luminous region is acceptable During filling It is desirable to keep the cavity phase constant for clean capture. Thanks to the reduced total voltage (6 MV) the present scheme can be kept with ultimate. HiLumi LHC/LARP Modulation of the cavity phase by the transient beam loading in physics. 2835 bunches, 1.7 10 11 p/bunch, 1.5 MV/cavity, QL=60k, full detuning (-7.8 kHz). Frascati, Nov. 15, 2012